Finite Group Databasebeta

C4×#14583665 #25960010

order11008
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#14583665

Splittings

FittingC2×C4×M16×C43 ⋊ C2
SylowC43 ⋊ C4×#568

Subgroups

subgroupG/H
centerC42C23×D43
commutatorC2×C43C23×C42
FrattiniC2×C4C24×D43
FittingC2×C4×M16×C43C2
socleC22×C43C24×C4
prime radicalC22×#10621898C22
cosocleC2×C4×C43C25
hypercenterC2×C4×M16D43
hypocenterC43C4×#568
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C4×M16

3250 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1816 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1032981);